Reprinted from pages 211-230 in A. A. Agrawal, S. Tuzun, and E.
Bent, editors. 1999. Inducible plant defenses against pathogens and
herbivores: Biochemistry, ecology, and agriculture. American
Phytopathological Society Press, St. Paul, MN (USA).
The Influence of Induced Plant Resistance on Herbivore
Population Dynamics
Nora Underwood
Abstract
Verbal and mathematical theory suggest that induced resistance in
plants may affect the long-term population dynamics of herbivores. However,
there is little direct empirical evidence that induced resistance affects herbivore
dynamics in the field. This chapter reviews both theoretical and empirical
evidence that induced resistance may affect herbivore population dynamics.
Methods for gathering new evidence, including the use of chemical elicitors,
natural damage and genotypic variation to manipulate induced resistance, are
also discussed. Finally, a simulation model of the interaction of induced
resistance and herbivore population dynamics that includes plant population
dynamics is presented. This model suggests that the relative number of
herbivore to plant generations in a system should strongly affect the influence of
induced resistance on herbivore population dynamics.
Introduction
Induced plant resistance to damage has clearly been shown to affect
both the behavior and performance of individual herbivores. Induced resistance
may also contribute to aspects of herbivore population dynamics such as
outbreaks, cycles, and population regulation that have long fascinated ecologists
(Cappuccino 1995). From the perspective of understanding herbivore population
dynamics, induced resistance can be defined as any change in a plant resulting
from damage and having a negative effect on herbivores (Karban and Baldwin
1997). Induced resistance is likely to be important for long-term herbivore
dynamics because in at least some systems, the strength of induced resistance is
a density dependent function of the amount of damage the plant receives (see
below). This density dependence makes induced resistance a potential source of
the negative feedback necessary to regulate herbivore populations (Rhoades
211
1985, Turchin 1990). Induced resistance that is delayed relative to the time of
damage might also increase the likelihood of fluctuations in herbivore
populations, because delayed density dependence has been shown to drive
cycles in population dynamics models (May 1973, Berryman et al. 1987).
Although it has frequently been suggested that induced resistance could be
responsible for regulating or driving cycles in herbivore populations (Benz
1974, Haukioja 1980, Rhoades 1985, Myers 1988), very few empirical or
theoretical studies have directly addressed the effects of induced resistance on
long-term herbivore population dynamics.
Empirical Evidence that Induced Resistance Affects Herbivore Population
Dynamics
Several kinds of indirect evidence can help us understand how induced
resistance may affect the population dynamics of herbivores. For example, we
can determine whether induced resistance affects herbivore characters such as
population growth rate or mortality, which influence population dynamics. We
can also ask whether the effects of induced resistance on herbivores are of the
type that might regulate herbivore populations (density dependent effects) or
produce cycles in those populations (delayed density dependence). However,
even if indirect evidence indicates that induced resistance has the potential to
influence herbivore populations, direct evidence is still required to demonstrate
that induced resistance alters long-term patterns of herbivore population
dynamics. In this section, direct and indirect empirical evidence for effects of
induced resistance on herbivore population dynamics are briefly reviewed (see
Karban and Baldwin 1997 for a recent review), and the pros and cons of
methods available for gathering further evidence are discussed.
Studies in both the lab and the field have demonstrated that induced
resistance affects herbivore performance characters (such as feeding preference,
growth rate, fecundity, and survival) that should influence herbivore population
size (Karban and Myers 1989, Karban and Baldwin 1997). This evidence
suggests that induced resistance has the potential to influence herbivore
population dynamics. Studies of herbivore populations over a few generations
have also demonstrated negative effects of induced resistance on aspects of
short-term dynamics such as population size or population growth rate (Karban
and Baldwin 1997).
There is also evidence that induced resistance is density dependent in
many systems (e.g., Karban and English-Loeb 1988, Baldwin and Schmelz
1994), and thus has the potential to regulate herbivore populations. For induced
resistance alone to regulate herbivore populations, it should be able to reduce
herbivore population growth rates to zero (Underwood 1999). How often
induced resistance is this strong is not yet clear, though in most studies effects
on herbivore performance are not very large (Karban and Baldwin 1997).
However, induced resistance could work in conjunction with other density
dependent influences, such as predation, to regulate herbivore populations
212
(Underwood 1999). There have as yet been no experimental demonstrations that
induced resistance regulates, or contributes significantly to regulating, any
population. While the influence of density dependence has been demonstrated in
herbivorous insect populations (e.g., Woiwood and Hanski 1992), this density
dependence has not been linked to induced resistance.
Theory suggests that for induced resistance to drive cycles in herbivore
populations, the effect of induced resistance on herbivores must be delayed
relative to herbivore generation time so that damage by herbivores in one
generation influences the performance of later generations (e.g., EdelsteinKeshet and Rausher 1989, Underwood 1999). Induced resistance can be delayed
either by a lag between damage and the induction of resistance or by slow decay
of induced resistance in the absence of further herbivory. Existing data on the
timing of induced resistance support the idea that induced resistance could
contribute to cycles in some herbivore populations (Karban and Baldwin 1997).
Studies of induced resistance in annual plants (e.g., Edwards et al. 1985,
Baldwin 1988a, Malcolm and Zalucki 1996, Underwood 1998) indicate that lag
and decay times are generally fairly short relative to herbivore generation times,
although even short lags might contribute to cycles in herbivores with very short
generation times (e.g., aphids or mites). Studies in several cycling forest systems
indicate that the decay of induced resistance can be substantially longer than
herbivore generation times (decays taking several years) (Baltensweiler 1985,
Haukioja and Neuvonen 1987). This indirect evidence suggests that induced
resistance may contribute to cycles in herbivore populations.
Although indirect evidence thus suggests that induced resistance might
affect long-term herbivore dynamics in at least some systems, there are very few
direct observations of effects on population dynamics in either the lab or the
field. This lack of data is understandable given the difficulty of studying
population dynamics directly (especially in the forest systems that may be
strongly influenced by induced resistance). The demonstrated effects on shortterm population size do indicate that induced resistance may be useful in
controlling pests on crops within a season (Karban 1991), and that induced
resistance has the potential to influence long-term dynamics in agricultural and
natural communities. However, these data cannot tell us whether induced
resistance actually affects the aspects of long-term population dynamics that
have excited the most interest in this field (regulation and cyclic fluctuation).
Techniques for Gathering Further Evidence
The ideal approach to evaluating the relative importance of induced
resistance and other factors in influencing the population dynamics of
herbivorous insects would be to conduct controlled experiments at the scale of
whole populations, in which induced resistance is manipulated and effects on
long-term population dynamics are observed. Unfortunately, experiments of this
sort would be prohibitively difficult in most systems. There are however, more
feasible approaches that can provide useful information about the effect of
213
induced resistance on long-term dynamics, including correlational studies, direct
observation of rapid-cycling herbivores, and density manipulation experiments.
Most studies that have explicitly addressed induced resistance and
long-term herbivore dynamics in the field have been carried out in forest
systems using techniques such as correlating herbivore dynamics with changes
in plant-quality (e.g., Benz 1974), and transplanting herbivores between
outbreaking and non-outbreaking populations (e.g., Myers 1981). These
techniques allow a high level of realism by examining herbivore dynamics at
very large scales, and comparing current conditions with existing long-term
census data. However, because induced resistance cannot be manipulated, the
precision with which the effects of induced resistance can be isolated from other
factors is limited in these studies.
Studying herbivores with very short generation times (such as aphids,
mites, whiteflies and thrips) might be one practical way to combine direct
observations of long-term dynamics with manipulation of induced resistance.
Several studies of induced resistance in systems with rapidly cycling herbivores
do contain data over what must be many herbivore generations (e.g., Karban
1986, Shanks and Doss 1989). However, these studies sample population size
only a few times - making it difficult to use these data to examine long-term
population dynamics. Many census data points are required to adequately
describe patterns of population dynamics, and particularly to assess effects on
regulation (Turchin 1997). More frequent sampling might allow for
characterization of within-season dynamics in these populations. However, since
populations of these insects are also strongly affected by seasonal patterns,
census data over many years may still be necessary to provide a true picture of
their dynamics (Harrison and Cappuccino 1995). Once long-term census data
are gathered, regardless of the generation time of the herbivore, several kinds of
information can be extracted. A number of methods can be used to detect the
regulating action of density dependence in census data, though this field has
been very contentious (Turchin 1997). The presence and periodicity of cycles
can be assessed from the autocorrelation function for the data (Berryman and
Turchin 1997). Finally, a population dynamic model can be fit to the data and
used to analyze the stability of the population dynamics (Edelstein-Keshet
1988).
In cases where direct observation of population dynamics is not
possible, density manipulation experiments allow estimation of long-term
dynamics from short-term (as little as one generation) population data. In this
type of design, populations with a range of initial densities are followed for one
or more generations, and data on initial density and density in the next
generation are used to construct a recruitment curve. This curve can be fit with a
discrete population dynamics model (such as the Ricker (Edelstein-Keshet 1988)
or Hassell (Hassell 1975) models), and the model can be analyzed to determine
the equilibrium population size, the stability of the equilibrium and tendency of
the population to cycle. For organisms with overlapping or continuous
generations, a similar approach could be used by fitting continuous population
214
dynamic models to census data, with the power of the method being improved
by combining data from populations initiated at several initial densities (Pascual
and Kareiva 1996).
Combination of density-manipulation with manipulation of induced
resistance would allow examination of the effect of induced resistance (or even
different levels or types of induced resistance) on the estimated long-term
dynamics of herbivore populations. Depending on the choice of system, this
design could incorporate effects at the scale of the whole population, or at much
smaller scales. Density manipulation approaches are only beginning to be used
in ecological experiments (Belovsky and Joern 1995, Underwood 1997), though
related techniques are standard in the management of fisheries (Roughgarden
1998). Harrison and Cappuccino (1995) discuss guidelines for this type of
experiment, and suggest that this technique should be more widely used to
search for population regulation.
Estimating long-term dynamics using density manipulation and model
fitting also has several drawbacks, one of which is that the experiments can be
very labor intensive. A more serious drawback is that using models fit to field
data in one generation to estimate dynamics over long periods of time assumes
that the parameters of the model will not change over time. This assumption
may be more valid for some systems than for others. For instance, the
characteristics of crop plants are likely to remain fairly constant from year to
year, as opposed to natural perennial plants whose characteristics may change
with age between years. Estimation of long-term dynamics is thus not suitable
for precise prediction of the size of particular populations over time, but should
allow examination of qualitative differences among populations subject to
different conditions.
Manipulating Induced Resistance
Whether population dynamics are directly observed or estimated, the
most rigorous experimental examination of the effects of induced resistance
requires the experimenter to manipulate induced resistance and create
appropriate controls. A new and appealing method of manipulation is the
application of chemical elicitors that cause the plant to produce induced
resistance. Because elicitors can be easily applied to the plant, and because their
effects are dose-dependent (Farmer and Ryan 1990, Baldwin et al. 1998),
elicitors have clear advantages in precision and ease of manipulation. However,
there are several drawbacks that might outweigh these advantages for studies of
the ecological effects of induced resistance. Some elicitors, jasmonic acid for
instance, have widespread effects on plant physiology (Creelman and Mullet
1997), so that the effects of elicitor-induced resistance could be confounded with
other physiological changes in the plant that are not normally caused by
herbivore feeding. Another potential drawback is that while elicitors can turn
plants “on” and keep them on via repeated application (Thaler et al. 1996), there
is nothing to prevent untreated plants from also being turned on by herbivores.
215
So while elicitors can create initially different conditions, any experiment that
runs long enough to allow “natural” induction might run into the problem of
elicitor and non-elicitor treatments converging in induction over time. This
problem may not materialize if elicitors produce larger responses than
herbivores do (Thaler et al. 1996), although if the induced resistance caused by
elicitors is outside the natural range of responses, results of experiments using
elicitors may not accurately reflect natural conditions.
It might be possible to correct the problem of induced and non-induced
treatments converging during an experiment by combining elicitors with
methods of inhibiting induced resistance. These methods include pot-binding,
which has been shown in at least one case to block induced resistance (Baldwin
1988b), and chemical inhibitors of induced resistance (Hartley 1988, Baldwin et
al. 1990, Stout et al. 1998). Pot-binding has the advantage of potentially
remaining effective throughout the experiment, thus maintaining differences
between treatment and control plants. Disadvantages of pot-binding are that it
has only been shown to work in one system, and it may affect aspects of the
plant’s physiology that influence herbivores in addition to induced resistance.
Like chemical elicitors of induced resistance, chemical inhibitors have the
potential drawback of affecting aspects of the plant’s physiology not normally
associated with induced resistance.
Another method of manipulating induced resistance levels is predamaging plants using either artificial damage (e.g., Edwards et al. 1985,
Hanhimaki 1989) or application of herbivores (e.g., Hanhimaki 1989, Shanks
and Doss 1989, Karban 1993, Agrawal 1998). The dynamics of herbivore
populations on pre-induced plants could then be compared with those on plants
that start out with no damage, and thus no induced resistance. Artificial damage
is relatively precise and easy to produce. However, a number of studies indicate
that in some systems artificial damage does not produce the same type or
strength of induced resistance as natural damage (Baldwin 1988a, Hanhimaki
1989). Using herbivores to produce the initial damage is logistically more
difficult, but has the virtue of being more likely to provoke the appropriate
induced response. Both methods of pre-damaging plants are subject to the
problem of convergence between induced and non-induced treatments during
the experiment.
An alternative approach for creating induced and non-induced
treatments is using genotypes of plants that inherently differ in their levels of
induced resistance. This technique is currently being used to examine the effects
of induced and constitutive resistance on herbivore population dynamics in time
(N. Underwood, unpublished data) and in space (W. Morris, unpublished data),
and has been used to look for relationships between induced and constitutive
resistance (Zangerl and Berenbaum 1991, Brody and Karban 1992, EnglishLoeb et al. 1998, N. Underwood, unpublished data). Among plant differences in
characters other than induced resistance could complicate the interpretation of
differences in herbivore dynamics among genotypes differing in induced
resistance. In theory, it should be possible through screening of genotypes,
216
breeding or transgenics, to obtain lines that are isogenic except for genes
controlling the production of induced resistance. Significant genetic variation for
induced resistance has been documented in several systems (e.g., Zangerl and
Berenbaum 1991, Brody and Karban 1992, English-Loeb et al. 1998, Agrawal,
this volume, N. Underwood, unpublished data). Agricultural systems, where
resistance and other characters have already been documented for a variety of
genotypes, may provide particularly convenient places to search for appropriate
genotypes. Once appropriate genotypes are located, using genotypic variation to
create treatments with high and low induced resistance is convenient, and
differences among treatments should be maintained throughout experiments. A
further advantage of this approach is that it allows consideration of evolutionary
as well as population dynamic questions.
Evidence from Mathematical and Simulation Models
Over the past three decades, many authors have presented verbal theory
concluding that induced resistance might regulate and drive cycles in herbivore
populations (Karban and Baldwin 1997). More recently, both analytical and
computer simulation modeling have been used to more rigorously explore the
interaction between induced resistance and herbivore populations. Some of these
models explicitly focus on effects of induced resistance on long-term population
dynamics (Fischlin and Baltensweiler 1979, Edelstein-Keshet and Rausher 1989,
Lundberg et al. 1994, Underwood 1999). Other models focusing on issues such
as the evolution of induced resistance (Frank 1993, Adler and Karban 1994), and
effects of induced resistance on the spatial dynamics of herbivores (Lewis 1994,
Morris and Dwyer 1997), also make predictions about temporal dynamics. The
predictions of these models vary with the type of plant-herbivore system they
model, suggesting that characteristics of the plant-herbivore system, such as the
strength and timing of induced resistance, mobility and selectivity of the
herbivore, and relative lengths of plant and herbivore generation times, will
affect the influence of induced resistance on herbivore population dynamics.
Results of existing models suggest that induced resistance has the
potential to regulate herbivore populations (i.e., prevent extinction and growth
without bound). Regulation is only possible when induced resistance can reduce
herbivore population growth rates to zero, and the probability of regulation tends
to increase with the strength of induced resistance, though regulation can also
depend on the timing of induced resistance, and the relative lengths of plant and
herbivore generations (Edelstein-Keshet and Rausher 1989, Underwood 1999).
The likelihood that induced resistance can produce cycles in herbivore
populations varies among models. Some models have found that induced
resistance by itself cannot produce persistent cycles, though it may produce
cycles that damp over time (Frank 1993, Adler and Karban 1994, Lundberg et
al. 1994, Morris and Dwyer 1997). Other models have found that induced
resistance drives persistent cycles in herbivore populations under certain
conditions (Fischlin and Baltensweiler 1979, Edelstein-Keshet and Rausher
217
1989, Lewis 1994, Underwood 1999). Both damping and persistent cycles are
associated with delays in the timing of induced resistance. The longer the delays
relative to herbivore generation time, the more likely cycles are, and the less
likely regulation becomes.
Induced resistance has been found in a very wide variety of plant-insect
systems, involving annual and perennial plants, and both uni- and multivoltine
insects. This raises the question of how the relative lengths of the generation
times of the plant and herbivore affect the impact of induced resistance on
herbivore dynamics. To examine this question, models need to include plant
population dynamics as well as herbivore dynamics. Adding plant dynamics to
models might increase the likelihood of cycling simply due to the interaction
between equations for the two populations, as occurs in some predator-prey
models (Edelstein-Keshet 1988). Several continuous time analytical models
have included plant population dynamics, with plant and herbivore generation
times equal in all cases (Frank 1993, Adler and Karban 1994, Lundberg et al.
1994). All three of these models have some tendency towards oscillation in plant
and herbivore populations, although plant dynamics are not discussed at length
for these models.
A Model Including Both Plant and Herbivore Population Dynamics
The simulation model of Underwood (1999) can be modified to
examine how variable plant population size and the relative lengths of plant and
herbivore generations affect the influence of induced resistance on herbivore
population dynamics. The model described in Underwood (1999) follows
individual plants and herbivores, and consists of three nested loops: a herbivory
loop (describing herbivore movement and feeding, and changes in induced
resistance in plants), a herbivore generation loop consisting of 30 herbivory
loops, and a plant reproduction loop consisting of variable numbers of herbivore
generations. There are two equations in the model. The first describes the level
of induced resistance in individual plant i at time t+1 (Ii,t+1) as a function of
damage to the plant, which is equal to the herbivore load on that plant (hi,(t-τ)):
(I i, t +1 =
αˆ
I i, t + αˆ )h i,(t − τ)
β
+ I i, t (1 − δ)
b + h i,(t − τ)
(1)
In this equation, β represents a physiological maximum induced resistance in an
individual plant, α̂ is the maximum increase in induced resistance at one time, b
is the half-saturation constant, δ is the decay rate of induced resistance and τ is
the lag time between damage and induced resistance. In this model it is assumed
that α̂ = β. The second equation describes herbivore population size in one
generation (Ht+g) as a function of its size in the previous generation (Ht) (where
one herbivore generation consists of g herbivory loops), the level of induced
218
resistance herbivores have encountered ( I ), and the strength of induced
resistance (critical level of induced resistance reducing herbivore reproduction
to zero, Ic):
H t + g = H t (1 + γ(1 −
I
))
Ic
(2)
where γ is the population rate of increase for herbivores.
To incorporate plant population dynamics, a third equation can be
added to the model. This equation describes the size of the plant population in
one generation (Pt+n*g) as a function of its size in the previous generation (Pt)
(where one plant generation consists of n * g herbivory loops), the average
damage incurred by plants ( D ), and the critical damage level reducing plant
reproduction to zero (Dc):
Pt + n*g = Pt (1 + λ(1 −
D P
- ))
Dc K
(3)
This formulation of plant reproduction assumes that there is no cost of induced
resistance to the plant. In this equation λ is the plant population growth rate and
K is a carrying capacity for the plant population set by factors other than
herbivore damage. D is calculated as the average damage to individual plants
in the population at one time (hi), averaged over all time steps in a plant
generation (n*g):
P
n *g
D=
¦
¦h
i =1
i
P
n *g
t =1
P
Because in this model all herbivores occupy a plant at all times,
¦h
i =1
i
= H . If
it is assumed that τ = 0, an equilibrium solution for this model can be found. At
equilibrium, Ii =
I = I*, H = H* and hi =
H*
= D . Substituting these into
P*
equations 1 and 2 and combining the two it can be shown that the equilibrium
conditions for H are γ = 0 and:
bI c δ
H*
=
*
α̂ − I c
P
(4).
Equation 4 implies that the ratio of herbivores to plants at equilibrium is a
constant (θ) determined by the properties of induced resistance. See Underwood
(1999) for a more detailed explanation of this model and its results, and
Underwood (1997) for derivation of the equilibrium condition. The equilibrium
219
conditions for the plant population are λ = 0 and:
H*
*
P * = K(1 − P ) .
Dc
(5).
Equation 5 implies that the equilibrium number of plants is determined by the
plant carrying capacity and the influence of herbivores on plants through
damage. Note that without an independent carrying capacity for plants (that is, if
the plant population is influenced only by herbivores), the model is unstable at
all points except Dc = θ.
The effect of induced resistance on herbivore and plant population
dynamics was explored by running simulations of the model. All runs had 30
herbivory loops per herbivore generation, and runs were started with initial plant
and herbivore populations of 100 individuals. Starting with different initial
population sizes did not change the behavior of the model. The effects of the
strength of induced resistance (Ic) and the critical damage level for plants (Dc)
on plant and herbivore populations were explored over a range of relative
numbers of herbivore to plant generations including 1:1, 10:1 and no plant
reproduction. The effects of lags in induced resistance (τ) were also considered.
For the runs reported here, all other parameters were held constant, with α and β
= 100, b = 10, γ = 2, λ = 1, δ = .07, and K = 100. These parameter values were
chosen largely arbitrarily (see Underwood 1999 for discussion of the
consequences of changing them).
All simulations were run for at least 150 herbivore generations, or long
enough for the output to converge on the asymptotic dynamics. Runs were not
replicated because initial exploration of the model indicated that there was not
appreciable variation among runs with the same parameter values. Data on
average plant and herbivore population sizes were calculated after the dynamics
reached their final state (when the behavior of plant and herbivore populations
was consistent over at least 50 generations). The behavior of the plant and
herbivore populations was divided into the following 5 categories: herbivore
extinction, stable herbivore and plant populations, damping cycles in the
herbivore population (with stable plants), cycles or fluctuations in the herbivore
population (with stable plants), both plants and herbivores cycling, and plant
extinction (caused by the uncontrolled increase of herbivores).
Results
Increasing the strength of induced resistance (decreasing Ic) decreases
herbivore population size in this model. Smaller herbivore populations allow the
plant population to grow, so that plant population size increases with increasing
strength of induced resistance (up to the plant carrying capacity K) (Fig. 1). The
effect of the strength of induced resistance (Ic) on herbivore and plant
populations is modified by the sensitivity of plant reproduction to herbivore
220
damage (Dc). As plants become more sensitive (Dc decreases), plant populations
Herbivore population size
1 000
8 00
6 00
4 00
2 00
0
0
50
100
0
50
100
Plant population size
1 00
Dc =
Dc =
Dc =
Dc =
Dc =
3
5
10
20
40
50
0
S tren gth of ind uc ed resistan ce (1 00 - I c )
Figure 1: Herbivore and plant population size as a function of the strength of induced
resistance. Dc (plant sensitivity to herbivore damage) is the critical damage level reducing
plant reproduction to zero. Each point results from a single simulation of the model with
one herbivores generation per plant generation and no lag in induced resistance. For these
results, plant carrying capacity (K) = 100.
decrease. Small plant populations lead to more herbivores per plant, which
causes induced resistance levels in the plants to rise and herbivore populations to
fall. The likelihood that herbivore populations are regulated (not extinct or
growing without bound) decreases as the number of herbivore generations per
plant generation decreases (Fig. 2). Induced resistance is least able to control
herbivore populations when herbivore and plant generation times are equal (Fig.
2C). When plants do not reproduce, lags in induced resistance decrease the
likelihood that the herbivore population is regulated, and increase the likelihood
of persistent cycles in the herbivore population at weaker levels of induced
resistance (Fig. 2A). When plants do reproduce, lags still have a destabilizing
effect on the herbivore population. As the lag time to induced resistance
increases, the likelihood that the herbivore population is unregulated (thus
driving plants extinct) or goes extinct (due to induced resistance) increases (Fig.
2B and C).
221
A
80
60
40
Strength of induced resistance (100 - Ic)
20
0
0
15
30
45
60
75
90
15
30
45
60
75
90
15
30
45
60
75
90
B 80
60
40
20
0
C
0
80
60
40
20
0
0
Lag (τ)
herbivore extinction
cycles (fluctuation within 10 point cycles for C)
damping cycles
stable (10 point cycles for C)
plant extinction, followed by herbivores
Figure 2: Long-term dynamic behavior of herbivore populations in simulations with A:
no plant reproduction, B: ten herbivore generations per plant generation, or C: one
herbivore generation per plant generation.
The large majority of the fluctuations exhibited by the model with plant
reproduction occur only in the herbivore population, and are forced by the
resetting of induced resistance to zero at the beginning of each plant generation.
These cycles only occur when herbivores have more than one generation per
plant generation (for example, 10 point cycles with 10 herbivore generations per
plant generation, Fig. 3A). The reason that cycles driven by lags in induced
222
A
600
100
400
50
200
0
0
20
40
60
80
0
105
B
200
95
100
85
0
Plants
Herbivores
300
100
75
0
20
40
60
80
300
100
C
100
200
90
100
0
0
40
60
80
20
H e r b iv o re g e n e ra tio n s
100
80
Figure 3: Cycles in the herbivore population forced by plant reproduction, and
fluctuations within those cycles, in individual runs of the model. A) and B) 10 herbivore
generations per plant generation, c) 30 herbivore generations per plant generation. A) Ic =
80, B) Ic = 60, C) Ic = 60, τ = 15 for all three runs.
resistance rarely occur with plant population dynamics included in the model is
that the effect of lags is complicated by the effect of the number of herbivore
generations per plant generation. As the number of herbivore generations per
plant generation increases, the likelihood of herbivore extinction decreases, and
fluctuations within the cycles forced by plant reproduction appear when induced
resistance is relatively strong (Ic is relatively low) (Fig. 3B). For example, with
10 herbivore generations per plant generation, there is a region in which the
smooth 10-point cycles forced by plant reproduction with relatively weak
induced resistance (Ic = 80) (Fig. 3A) are replaced by oscillations with two
peaks, one larger and one smaller (Fig. 3B). This second peak is due to a
damping oscillation in the herbivore population that is interrupted every 10
generations. These damping oscillations are more apparent if the number of
herbivore generations per plant generation is increased (Fig. 3C). These
fluctuations within the cycles forced by plant reproduction occur at weaker
levels of induced resistance as the lag time gets longer, just as stable and longer
damping cycles occur at weaker levels of induced resistance as the lag time gets
longer without plant population dynamics.
223
Initial explorations of this model indicate that it is very rare for the
interaction between herbivores and plants in this model to produce joint
fluctuations in the plant and herbivore populations. Plant populations remain
stable in most configurations of the model because the effect of herbivores on
plants is generally either very small, or so large that it drives the plants extinct
(Fig. 4A). The effect of herbivores on plants in this model is represented by D ,
the amount of damage each plant receives. As shown above, at equilibrium, D =
H * P * = θ (the constant describing the characteristics of induced resistance).
The relationship between D and Ic (the strength of induced resistance) is
exponential (Fig. 4A). This means that at most levels of Ic herbivores have
relatively little effect on plants, but as Ic increases the effect of herbivores on
plants suddenly becomes very large, generally driving the plant population
extinct. Persistent cycles occur only in the region between little effect and
extinction, and because of the steeply accelerating curve, that region is very
small. For example, in Fig. 4B, joint fluctuations of plants and herbivores are
found only along a single line dividing stable herbivore and plant populations
from plant extinction.
In summary, the following results arise from this model of induced
resistance and plant and herbivore population dynamics. First, the interaction
between plant and herbivore populations very rarely results in cycling in both
populations. Second, the most frequent cycles produced in this model are
herbivore population cycles forced by plant reproduction. This result suggests
that herbivores with rapid generation times relative to their host plants might be
expected to exhibit cyclic dynamics more frequently than herbivores whose
generation time is close to the generation time of their host. These forced cycles
would, however, only be expected in cases where plant recruitment is relatively
synchronous, such as in annual plants, or in perennials whose level of induced
resistance is returned to zero when the plant dies back (due to winter or a dry
season) and then re-grows. In the field, these cycles would happen within a
season, and would be most likely to occur in rapid cycling insects or mites. Such
patterns are observed, but are difficult to distinguish from patterns driven by
environmental factors such as temperature (see Underwood 1999).
Lags in this model reduce the stability of plant and herbivore
populations. However, other than cycles forced by plant reproduction, induced
resistance rarely drives cycles in the herbivore or plant populations regardless of
lag time, although at intermediate strengths of induced resistance the forced
cycles can be complicated by internal fluctuations, giving the appearance of
complex behavior.
A clear, though not very surprising, outcome of this model is that the
relative number of herbivore to plant generations strongly affects the influence
of induced resistance on herbivore population dynamics. A higher number of
herbivore generations per plant generation generally increases stability, and also
increases the likelihood of stable cycles (both forced and otherwise). This
observation suggests that systems with many herbivore generations per plant
224
generation should be more likely to show stable cycles than systems with very
25
25
A
D
20
20
c
15
15
s
10
10
s
55
00
Simulation results
Theoretical results
e
s
s
e
Strength of induced
resistance (100 - Ic)
00
40
60
80
100
20
20
40
60
80
100
Strength of induced resistance (100-Ic)
B
•
80 •
60
40
•
20
0
•
0
15 30 45 60 75 90
Lag (τ)
herbivore ext inction
stable
plant extinction (followed by herbivores)
joint cycles in herb ivore and plant populations
Figure 4: A. Relationship between the strength of induced resistance (Ic) and the
influence of herbivores on plants ( D ). Points on the line indicate equilibrium value of D
for single runs of the model. Letters above points indicate dynamic behavior of herbivore
and plant populations at each point (s = stable, c = cycles, e = extinct), and the dotted line
indicates the relationship predicted by the equations in the model. B. Dynamic behavior
of herbivore and plant populations over a range of strengths of induced resistance and lag
times, with one herbivore generation to each plant generation. Boxes indicate joint cycles
in the plant and herbivore population for lags of 0, 8, and 15 herbivory loops.
few herbivore generations per plant generation. In fact, all observations of longterm cycles in insect herbivore populations that have been attributed
(tentatively) to induced resistance occur in systems with long-lived trees and
short-lived herbivores (Karban and Baldwin 1997). It is important to emphasize
that it is the relative number of herbivore and plant generations that should be
considered in predicting the effects of induced resistance on population
225
dynamics, rather than whether the herbivore is univoltine versus multivoltine, or
the plant is annual versus perennial.
Synthesis
The ecological literature includes many discussions, both theoretical
and empirical, of how induced resistance should affect short and long-term
herbivore population dynamics. There is, however, very little direct evidence
that induced resistance can either regulate or drive cycles in herbivore
populations. Although the current lack of data arises largely from the difficulty
of approaching this issue experimentally, there is a range of techniques, some of
which have only recently been developed, that should allow researchers to
empirically address the effects of induced resistance on herbivore population
dynamics. Future empirical studies could be guided by existing theoretical
explorations of induced resistance and herbivore dynamics, which make some
broad predictions for when induced resistance might regulate or drive cycles in
herbivore populations. For example, theory predicts that cycles should be more
frequent with delays in either the onset or decay of induced resistance.
Measuring the timing of induced resistance in the field will be difficult with
long-lived plants, but is conceptually straightforward (Underwood 1998), so that
the dynamics of herbivore populations in systems with longer versus shorter lag
or decay times could be compared. The model presented here provides further
predictions of how relative generation times might affect the likelihood of
cycles. These predictions remain to be tested. In general, the study of induced
resistance and herbivore population dynamics would benefit from a wider use of
controlled experiments and model fitting.
Future Directions
Just as induced resistance may affect the population dynamics of
herbivores, it may have important effects on the population dynamics of plant
pathogens. Because plant pathogens are so much smaller and faster reproducing
than their hosts, induced resistance likely affects pathogen population dynamics
at two scales: within- and among-hosts. However, most models and studies of
plant disease dynamics address only among host dynamics, leaving the
dynamics of the disease within the host, as well as plant population dynamics,
unknown (Thrall et al. 1997). Results from metapopulation theory suggest that
taking into account local (within host) dynamics might change predictions for
among host dynamics (e.g., Hastings and Wolin 1989). Because herbivores and
pathogens are nearly always both present in plant populations, it would also be
valuable to determine how pathogens and herbivores affect each other’s
population dynamics. The importance of this interaction should depend in part
on the specificity of the plant’s induced responses (Stout and Bostock, this
226
volume).
The effect of induced resistance on herbivore spatial dynamics also
deserves further attention. The few spatially explicit models of induced
resistance and herbivore dynamics (Lewis 1994, Morris and Dwyer 1997)
suggest that induced resistance may affect herbivore spread differently from
constitutive resistance. Few empirical studies have addressed the effect of
induced resistance on herbivore movement (e.g., Harrison and Karban 1986, W.
Morris, unpublished data) and these have considered relatively small scales.
Studies that examine how induced resistance and herbivore characters such as
mobility and selectivity interact to determine herbivore spatial distributions
could shed light on pest movement as well as the dispersion of native herbivores
in natural systems.
Finally, although there is evidence for genetic variation in induced
responses from several systems, most discussions of induced resistance and
herbivore population dynamics have not explicitly considered variation in
induced responses among plants. It would be interesting to determine how
variation among plants affects the influence of induced resistance on herbivore
population dynamics, especially for systems with selective herbivores.
Understanding the effects of population genetic variation for resistance
characters such as induced resistance may help evaluate the application of mixed
cropping systems in agriculture, as well as improving our understanding of
natural systems. Considering variation in induced resistance may also provide an
opportunity to link population dynamics and evolution in plant-herbivore
systems.
Acknowledgements
I thank A. Agrawal, B. Inouye, R. Karban, M. Rausher, M. Sabelis, P.
Tiffin and J. Thaler for thoughtful discussions and helpful editing. This work
was supported by NSF DEB grant #9615227 to M. Rausher and by NRI
Competitive Grants Program/USDA award #98-35302-6984 to N. Underwood.
Literature Cited
Adler, F. R., and R. Karban. 1994. Defended fortresses or moving targets? Another model of
inducible defenses inspired by military metaphors. American Naturalist 144:813-832.
Agrawal, A. A. 1998. Induced responses to herbivory and increased plant performance. Science
279:1201-1202.
Baldwin, I. T. 1988a. The alkaloidal responses of wild tobacco to real and simulated herbivory.
Oecologia 77:378-381.
Baldwin, I. T. 1988b. Damage-induced alkaloids in tobacco: pot-bound plants are not inducible.
Journal of Chemical Ecology 4:1113-1120.
Baldwin, I. T., D. Gorham, E.A. Schmeltz, C.A. Lewandowski, G.Y. Lynds. 1998. Allocation of
nitrogen to an inducible defense and seed production in Nicotiana attenuata. Oecologia
115:541-552.
Baldwin, I. T., and E. A. Schmelz. 1994. Constraints on an induced defense: the role of leaf area.
Oecologia 97:424-430.
227
Baldwin, I.T., Sims, C.L. and S.E. Kean. 1990. The reproductive consequences associated with
inducible alkaloidal responses in wild tobacco. Ecology 71:252-262.
Baltensweiler, W. 1985. On the extent and the mechanisms of the outbreaks of the larch budmoth
(Zeiraphera diniana Gn., Lepidoptera, Tortricidae) and its impact on the subalpine larchcembran pine ecosystem. Pages 215-219 in H. Turner and W. Tranquillini, editors.
Establishment and Tending of Subalpine Forest: Research and Management. Swiss Federal
Institute of Forestry Research, Birmensdorf, Switzerland.
Belovsky, G. E., and A. Joern. 1995. The dominance of different regulating factors for rangeland
grasshoppers. Pages 359-386 in N. Cappuccino and P. W. Price, editors. Population
Dynamics: New Approaches and Synthesis. Academic Press, New York.
Benz, G. 1974. Negative feedback by competition for food and space, and by cyclic induced changes
in the nutritional base as regulatory principles in the population dynamics of the larch
budmoth, Zeiraphera diniana (Guenee)(Lep., Tortricidae). Zeitschrift fur Angewandte
Entomologie 76:196-228.
Berryman, A. A., N. C. Stenseth, and A. S. Isaev. 1987. Natural regulation of herbivorous forest
insect populations. Oecologia 71:174-184.
Berryman, A. and T. Turchin 1997. Detection of delayed density dependence: comment. Ecology
87:318-320.
Brody, A. K., and R. Karban. 1992. Lack of a tradeoff between constitutive and induced defenses
among varieties of cotton. Oikos 65:301-306.
Cappuccino, N. 1995. Novel approaches to the study of population dynamics. Pages 3-16 in N.
Cappuccino and P. W. Price, editors. Population Dynamics: New Approaches and Synthesis.
Academic Press, San Diego.
Creelman, R. A., and J. E. Mullet. 1997. Biosynthesis and action of jasmonates in plants. Annual
Review of Plant Physiology and Plant Molecular Biology 48:355-381.
Edelstein-Keshet, L. 1988. Mathematical Models in Biology. Random House, New York.
Edelstein-Keshet, L., and M. D. Rausher. 1989. The effects of inducible plant defenses on herbivore
populations. 1. Mobile herbivores in continuous time. American Naturalist 133:787-810.
Edwards, P. J., S. D. Wratten, and H. Cox. 1985. Wound-induced changes in the acceptability of
tomato to larvae of Spodoptera littoralis: a laboratory bioassay. Ecological Entomology
10:155-158.
English-Loeb, G., R. Karban, and M. A. Walker. 1998. Genotypic variation in constitutive and
induced resistance in grapes against spider mite (Acari: Tetranychidae) herbivores.
Environmental Entomology 27:297-304.
Farmer, E.E. and C.A. Ryan. 1990 Interplant communication: airborne methyl jasmonate induces
synthesis of proteinase inhibitors in plant leaves. Proceedings of the National Academy of
Science USA 87:7713-7716.
Fischlin, A., and W. Baltensweiler. 1979. Systems analysis of the larch budworm system. Part I. The
larch-larch budmoth relationship. Pages 273-289 in B. Delucchi and W. Baltensweiler,
editors. IUFRO Conference, Zurich, Switzerland.
Frank, S. A. 1993. A model of inducible defense. Evolution 47:325-327.
Hanhimaki, S. 1989. Induced resistance in mountain birch: defence against leaf-chewing insect guild
and herbivore competition. Oecologia 81:242-248.
Harrison, S., and N. Cappuccino. 1995. Using density-manipulation experiments to study population
regulation. Pages 131-147 in N. Cappuccino and P. W. Price, editors. Population Dynamics:
New Approaches and Synthesis. Academic Press, San Diego.
Harrison, S., and R. Karban. 1986. Behavioral response of spider mites (Tetranychus urticae) to
induced resistance of cotton plants. Ecological Entomology 11:181-188.
Hartley, S.E. 1988. The inhibition of phenolic biosynthesis in damaged and undamaged birch foliage
and its effect on insect herbivores. Oecologia 76:65-70.
Hassell, M. P. 1975. Density-dependence in single-species populations. Journal of Animal Ecology
44:283-295.
Hastings, A., and C. L. Wolin. 1989. Within-patch dynamics in a metapopulation. Ecology 70:12611266.
Haukioja, E. 1980. On the role of plant defences in the fluctuation of herbivore populations. Oikos
35:202-213.
228
Haukioja, E., and S. Neuvonen. 1987. Insect population dynamics and induction of plant resistance:
the testing of hypotheses. Pages 411-432 in P. Barbosa and J. C. Schultz, editors. Insect
Outbreaks. Academic Press, Inc., San Diego.
Karban, R. 1986. Induced resistance against spider mites in cotton: field verification. Entomologia
Experimentalis Et Applicata 42:239-242.
Karban, R. 1991. Inducible resistance in agricultural systems. Pages 403-419 in D. W. Tallamy and
M. J. Raupp, editors. Phytochemical Induction by Herbivores. Wiley and Sons, New York.
Karban, R. 1993. Induced resistance and plant density of a native shrub, Gossypium thurberi, affect
its herbivores. Ecology 74:1-8.
Karban, R., and I. T. Baldwin. 1997. Induced Responses to Herbivory. University of Chicago Press,
Chicago.
Karban, R., and G. M. English-Loeb. 1988. Effects of herbivory and plant conditioning on the
population dynamics of spider mites. Experimental and Applied Acarology 4:225-246.
Karban, R., and J. H. Myers. 1989. Induced plant responses to herbivory. Annual Review of Ecology
and Systematics 20:331-348.
Lewis, M. A. 1994. Spatial coupling of plant and herbivore dynamics: the contribution of herbivore
dispersal to transient and persistent "waves" of damage. Theoretical Population Biology
45:277-312.
Lundberg, S., J. Järemo, and P. Nilsson. 1994. Herbivory, inducible defence and population
oscillations: a preliminary theoretical analysis. Oikos 71:537-539.
Malcolm, S. B., and M. P. Zalucki. 1996. Milkweed latex and cardenolide induction may resolve the
lethal plant defence paradox. Entomologia Experimentalis et Applicata 80:193-196.
May, R. M. 1973. Stability and Complexity in Model Ecosystems. Princeton University Press,
Princeton.
Morris, W. F., and G. Dwyer. 1997. Population consequences of constitutive and inducible plant
resistance: herbivore spatial spread. American Naturalist 149:1071-1090.
Myers, J. H. 1981. Interactions between western tent caterpillars and wild rose: A test of some
general plant herbivore hypotheses. Journal of Animal Ecology 50:11-25.
Myers, J. H. 1988. The induced defense hypothesis: does it apply to the population dynamics of
insects? Pages 345-365 in K.C. Spencer, editor. Chemical Mediation of Coevolution.
Academic Press, San Diego.
Pascual, M.A. and P. Kareiva. 1996. Predicting the outcome of competition using experimental data:
maximum likelihood and bayesian approaches. Ecology 77:337-349.
Rhoades, D. F. 1985. Offensive-defensive interactions between herbivores and plants: their
relevance in herbivore population dynamics and ecological theory. American Naturalist
125:205-238.
Roughgarden, J. 1998. How to manage fisheries. Ecological Applications 8:s160-s164.
Shanks, C. H., and R. P. Doss. 1989. Population fluctuations of twospotted spider mite (Acari:
Tetranychidae) on strawberry. Environmental Entomology 18:641-645.
Stout, M.J., K.V. Workman, R.M. Bostock and S.S. Duffey. 1998. Stimulation and attenuation of
induced resistance by elicitors and inhibitors of chemical induction in tomato (Lycopersicon
esculentum) foliage. Entomologia Experimentalis et Applicata 86:267-279.
Thaler, J.S., M.J. Stout, R. Karban, S.S. Duffey. 1996. Exogenous jasmonates simulate insect
wounding in tomato plants (Lycopersicon esculentum) in the laboratory and field. Journal of
Chemical Ecology 22:1767-1781.
Thrall, P.H., J.D. Bever, J.D. Mihail, H.M. Alexander. 1997. The population dynamics of annual
plants and soil-borne fungal pathogens. Journal of Ecology 85:313-328.
Turchin, P. 1990. Rarity of density dependence or population regulation with lags? Nature 344:660663.
Turchin, P. 1997. Population regulation: old arguments and a new synthesis. Pages 19-40 in N.
Cappuccino and P.W. Price, editors. Population Dynamics: New Approaches and Synthesis.
Academic Press, New York.
Underwood, N. 1997. The interaction of plant quality and herbivore population dynamics. Ph.D.
dissertation, Duke University, Durham NC.
Underwood, N. C. 1998. The timing of induced resistance and induced susceptibility in the soybean
Mexican bean beetle system. Oecologia 114:376-381.
229
Underwood, N. C. 1999. The influence of plant and herbivore characteristics on the interactions
between induced resistance and herbivore population dynamics. American Naturalist
153:282-294.
Woiwood, I. P., and I. Hanski. 1992. Patterns of density dependence in moths and aphids. Journal of
Animal Ecology 61:619-629.
Zangerl, A. R., and M. R. Berenbaum. 1991. Furanocoumarin induction in wild parsnip: genetics and
populational variation. Ecology 71:1933-1940.
230